Who cares what the other graduates think of your university choice? Their opinion is not relevant to your career nor your employment prospects.
The fact that you are employed on exactly the same graduate training scheme as them (doing the same job and earning exactly the same money as them), should be evidence enough that your university doesn't matter. The people who hired you for the job didn't think it mattered, and you've already been told by one of the senior developers (who has far more experience than the other graduates) that it doesn't matter.
Another way to look at it -- those people went to a university which is supposedly much better than the one you went to, yet they are at the same stage in their life and career as you, which means they aren't going to progress any more quickly than you nor end up being paid more as a result either, so what difference did it make to them in going to that better Uni? The answer is 'none'.
Assuming that you're successful in your career over the next 2-3 years, the relevance of your education background will rapidly decrease in-line with the skills and experience you gain working for your employer on their project(s) and the tasks you're asked to do. Anything you'd have learned at university will be very quickly be overtaken by the new things you learn during this time.
Taking a second computer science degree won't teach you anything that you're not already going to learn over the next 2-3 years by working in your job (again, assuming you're successful and that you don't stagnate). To that end, a second degree won't do anything to boost your employment prospects, and would probably be harmful because it will set your career back by 3 years in repeating a lot of content you've already studied, and you'll be paying £9k per year.